5. Two points are 10 units apart on the coordinate plane. If

Mathematics

1 answer:

eimsori [14]4 years ago

3 0

Answer:

Step-by-step explanation:

Let's say the ant is walking across the floor. Then it hits the wall and starts climbing to the ceiling.

We have a right triangle, as in the diagram, so we can apply Pythagoras' Theorem.

x² + 6² = 10²

x² + 36 = 100

x² = 64

x = 8

The ant must walk eight vertical units.

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Which expression represents the value of 5 nickels and x dimes?

Llana [10]

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5(0.05) + 0.10x

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3 years ago

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A gardener wants to make a rectangular enclosure using a wall as one side and 120 m of fencing for the other three sides. expres

Solnce55 [7]

The area is given by A = -2x² + 120x. The greatest area is given by x = 30 m.

Explanation:
See the picture attached for reference.

Let's call:
x = side not facing the wall
We know that the total fence is 120m, therefore
(120 - 2x) = side facing the wall

Note: you could choose to be x = side facing the wall, but the calculations would be a little bit more complicated.

We can now calculate the area of a rectangle:
A = b · h =
= x · (120 - 2x)
= -2x² + 120x

In order to find a maximum for this function, we need to calculate the first derivative:
$\frac{d}{dx} (-2x^{2} + 120x ) = -4x +120$

Then, we need to find the candidate points by setting the derivative equal to zero:
-4x +120 = 0
-4(x - 30) = 0
x = 30

Now, in order to understand if the candidate point is a maximum or a minium, let's calculate the second derivative:

 $\frac{d}{dx}(-4x + 120) = -4$ 

According to the "Second Derivative Test", if the second derivative is negative, the point is a local maximum.

Hence, x = 30m gives the greatest area, and we would have:
side not facing the wall = 30m
side facing the wall = 120 - 2·30 = 60m
area = 30 · 60 = 1800 m²